A Parametric Study of a Solar-Assisted House Heating System with a Seasonal Underground Thermal Energy Storage Tank

Home , Central solar heating, Heating system, Room temperature

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Article A Parametric Study of a Solar-Assisted House Heating System with a Seasonal Underground Thermal Energy Storage Tank

Le Minh Nhut 1, Waseem Raza 2 and Youn Cheol Park 3,*

1 Department of Thermal Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 700000, Vietnam; [email protected] 2 Graduate School of Mechanical Engineering, Jeju National University, Jeju 63243, Korea; [email protected] 3 Department of Mechanical Engineering, Jeju National University, Jeju 63243, Korea * Correspondence: [email protected]

Received: 15 July 2020; Accepted: 16 October 2020; Published: 20 October 2020

Abstract: The requirement for energy is increasing worldwide as populations and economies develop. Reasons for this increase include global warming, climate change, an increase in electricity demand, and paucity of fossil fuels. Therefore, research in renewable energy technology has become a central topic in recent studies. In this study, a solar-assisted house heating system with a seasonal underground thermal energy storage tank is proposed based on the reference system to calculate the insulation thickness eﬀect, the collector area, and an underground storage tank volume on the system performance according to real weather conditions at Jeju Island, South Korea. For this purpose, a mathematical model was established to calculate its operating performance. This mathematical model used the thermal response factor method to calculate the heat load and heat loss of the seasonal underground thermal energy storage tank. The results revealed that on days with diﬀerent weather conditions, namely, clear weather, intermittent clouds sky, and overcast sky, the obtained solar fraction was 45.8%, 17.26%, and 0%, respectively. Using this method, we can save energy, space, and cost. This can then be applied to the solar-assisted house heating system in South Korea using the seasonal underground thermal energy storage tank.

Keywords: energy; heating system; solar energy; underground thermal storage tank

1. Introduction Domestic hot water and space heating production in residential buildings provides roughly 60% of the total energy requirement in cold climate nation-states and about 43% in modest and warm weather countries in 2010 [1]. Recently, global energy consumption has increased signiﬁcantly, especially concerning hydrocarbon deposit-based energies. Therefore, the fast and intensive use of hydrocarbons causes substantial damage, threatens the energy supply chain, and raises energy prices and environmental pollutions. Such economic and environmental issues drive the quest for alternative ways of providing energy sources, which requires conversion to clean and sustainable renewable energy assets that will never be exhausted. Renewable energy technologies currently account for about 13.3% of universal energy needs [2,3]. Solar energy is a fascinating technology amid all other renewable energies that absorb and transform abundant energy from the sun into useable energy. Evacuated tube collectors (ETC) transform solar energy to heat that can be applied to residential and commercial buildings in space or water heating and air conditioning. The energy needs for space heating of buildings can be supplied by solar radiation, employing various arrangements from the seasonal underground thermal energy

Sustainability 2020, 12, 8686; doi:10.3390/su12208686 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 8686 2 of 19 storage tank (SUTEST) [4]. SUTEST is a feasible solution to resolve the inconsistency concerning heat supply and demand. In the meantime, it is used to store heat on an hourly, daily, weekly, and seasonal basis and thus is contributes towards a worldwide energy conversion [5]. It has already been described as one of the safest, most efficient, and most cost-effective space heating and cooling systems [6]. The capacity of thermal energy storage tanks needs to be increased to advance the efficiency of solar-assisted heating systems. Nevertheless, due to space constraints, the installation of large storage tanks in a small-family house is often limited. There are many constraints, limiting the possibility of utilizing the large stores such as the area of the rooftop, the ceiling height of the basement, the dimension of the entrance, etc. Recently, there has been a trend to utilize the underground storage in a house as a SUTEST for solar-assisted heating systems to raise the consumption of solar thermal energy using seasonal solar thermal energy storage. Solar energy is an essential source of renewable energy to the solar heating systems, but the problem limits its use as a time-dependent source of energy. If the energy supply occurs at different times due to demands, some energy can be lost [7]. When the solar-assisted heating system with a seasonal underground thermal energy storage tank is built, the system can be charged during the summertime, for example, via solar thermal output, and can be stored for future use throughout the cold wintertime [8,9]. Dincer [10,11] dealt with the approaches and uses of identification, evaluation, and usage of thermal energy storage systems, in addition to the economic, energy preservation, and eco-friendly aspects of such systems. Theoretically, Inalli et al. [12] researched a domestic heating system due to solar energy stored in a spherical underground tank. Ucar and Inalli [13] used the finite element method to evaluate the efficiency of solar heating systems using seasonal storages. Utilizing a MATLAB computer code, they resolved heat transfer problems as a function of time among storage, surrounding ground, and the measured transient temperature distribution inside the ground surrounding the tank. They witnessed a rise in storage temperature and a drop-in storage volume with a rise in the collector area. Nordell and Hellstrom [14] achieved a 60% solar fraction (solar energy is 60% of the total heat demand) for a compound of 90 small houses with an entire heat demand of 1080 MWh, 2 a source temperature of 30 ◦C and a solar collector area of 3000 m . Qu and Yin [15] considered the design, installation, modeling, and testing of a solar-based thermal system that could theoretically provide 39% of cooling and 20% of the heating load for building space, respectively. Regarding the comprehensive exploration of seasonal thermal energy storage constructed from residential solar installations and prototypes, most of the current plans are in Denmark [16,17], Germany [18,19], Sweden [20], China [21–23], Canada [24,25], and the United States [26]. Among these, some researchers established the TRNSYS model for the project that is used to examine the seasonal thermal energy storage (STES) system proficiency. Building an underground thermal energy storage tank (UTEST) on a fairly large scale with a minimum volume of 20,000 m3 is advantageous for storing and extracting heat seasonally and reducing capital cost. Besides, large-scale STES schemes are most effective regarding technological capability and financial sustainability [27]. In addition, Willasmil et al. [28] analyzed and discussed in depth the methods used to enclose STES with insulation materials. The properties’ characteristics and comparative costs were reported for insulating materials suitable for TES up to 90 ◦C. Accordingly, a large-scale and long-span TES allows for a more robust and easier deployment of solar-energy and has advantages concerning lower fossil fuel usage and immediate higher energy savings and lower emissions [29,30]. Li et al. [31] presented the control strategies for the solar collector system to improve a solar heating system’s performance with underground pit seasonal storage in the non-heating season. Yumrutas and Unsal evaluated the annually periodic operation condition and long-term performance of a solar-assisted house heating system with a heat pump and an underground energy storage tank [32]. This study aims to evaluate the insulation thickness effect, the collector area, and, the volume of SUTEST through system performance. To calculate the operation performed using the thermal response factor method, an accurate systematic model is constructed to calculate the heating capacity Sustainability 2020, 12, 8686 3 of 19

Sustainability 2020, 12, x FOR PEER REVIEW 3 of 19 of a residential building and the heat loss of the underground thermal storage tank. As solar fraction increases,increases, the operating operating cost cost automatically automatically decre decreasesases due due to the to theenergy energy saving. saving. The parametric The parametric effects eforﬀects the for SUTEST the SUTEST performance performance are discussed are discussed,, and and they they are are expected expected to to be be use usefulful for upcomingupcoming enhancementenhancement work.work.

2.2. MaterialsMaterials andand MethodsMethods

2.1.2.1. ReferenceReference Solar-AssistedSolar-Assisted HouseHouse HeatingHeating SystemSystem TheThe referencereference solar-assistedsolar-assisted househouse heatingheating systemsystem isis presentedpresented inin FigureFigure1 1,, which which is is designed designed andand installedinstalled onon aa JejuJeju IslandIsland home’shome’s rooftop.rooftop. TheThe latitude,latitude, longitude,longitude, andand altitudealtitude ofof JejuJeju IslandIsland areare 3333◦°3131′0 North, 126126◦°3232′0 EastEast,, and 8 m elevation above the sea level.level. This system comprises anan evacuated 2 tubetube collector,collector, hashas aa totaltotal collectioncollection surfacesurface areaarea ofof26 26 mm2 andand waswas installedinstalled withwith aa 4545◦° tilttilt angleangle withwith respectrespect toto thethe horizontalhorizontal planeplane towardstowards thethe south,south, aa thermalthermal storagestorage tanktank ofof 1.21.2 mm33, a ann auxiliary boiler, andand thethe heatingheating panels,panels, asas shownshown inin FigureFigure1 1.. In In this this reference reference system, system, via via the the heat heat exchanger exchanger in in the the collectorcollector loop, loop the, the useful useful heat heat gain gain from from the evacuatedthe evacuated tube collectors tube collectors is conveyed is conveyed by the solar by the collector solar tocolle thector storage to the tank. storage In tank the case. In the of case hot waterof hot inwater the in home, the home if the, if exit the temperature exit temperature does does not hitnot the hit requiredthe required temperature temperature it is heatedit is heated by the by boiler the bo andiler provided and provided to the user.to the In user. the case In the of space case of heating, space theheating, hot water the hot in water the storage in the tank storage is delivered tank is delivered through through the panels the hidden panels inhidden each room’sin each ﬂoorroom’s spaces. floor Whenspaces. the When hotwater the hot temperature water temperature is adequately is adequately high, the high, energy the is energy extracted is extracted from the from thermal the thermal storage tank;storage conversely, tank; conversely if the hot, if water the hot temperature water temperature is lower thanis lower the appropriatethan the appropriate temperature, temperature, the boiler the is turnedboiler is on, turned and hot on water, and hot is supplied water is straight supplied to straight the panels. to the For panels. the auxiliary For the boiler, auxiliary the fuel boiler, is kerosene, the fuel andis kerosene the boiler, and eﬃ theciency boiler is assumed efficiency to is be assumed 80%. The to fuel be 80%. density The is fuel 0.839 density kg/m3 isand 0.839 the kg/m lower3 heatingand the valuelower is heating 42,886 value kJ/kg. is 42,886 kJ/kg.

Figure 1. Illustration of a reference solar-assisted house heating system. Figure 1. Illustration of a reference solar-assisted house heating system. The general view of the proposed and investigated system for a residential house based on the referenceThe solargeneral assisted view of house the proposed heating system and investigated is shown in system Figure2 for. The a residential operation ofhouse this systembased on is the as reference solar assisted house heating system is shown in Figure 2. The operation of this system is as follows. The water temperature in the SUTEST is maintained at a minimum value of 50 ◦C to ensure spacefollows. heating The water supply, temperature even during in the daytimeSUTEST andis maintained for domestic at a hotminimum water with value low of solar50 °C radiation.to ensure Dependingspace heating on supply the desires, even of during residential the day proprietors,time and for four domestic different hot approaches water with were low designed solar radiation in the. presentDepending study. on Thethe desire first loops of isresidential the heat additionproprietors in,which four different the captured approaches solar energy were designed is transmitted in the frompresent the study. solar collector The first to loop the SUTESTis the heat through addition the in heat which exchanger the captured in the collectorsolar energy loop sinceis transmitted the tank temperaturefrom the solar is collector much lower to the than SUTEST the outlet through temperature the heat exchanger of the solar in collector. the collector The loop second since loop the is tank the heattemperature extraction, is much an open-loop lower than for domesticthe outlet water temperature supply usedof the to solar get thermal collector. energy The second from the loop SUTEST is the heat extraction, an open-loop for domestic water supply used to get thermal energy from the SUTEST and deliver it to users. The required domestic hot water temperature is fixed at 45 ◦C. In the third loop, theand heat deliver addition it to takesusers. place The re suchquired that domestic the boiler hot transfers water heattemperature from the combustionis fixed at 45 process °C. In ofthe fuel third to theloop working, the heat fluid addition (water). takes The place working such fluid that isthe then boiler pumped transfers to the heat SUTEST from the via combustion the heat exchanger process inof thefuel boiler to the loop. working The boiler fluid loop(water). pump The switched working on fluid since is the then SUTEST pumped temperature to the SUTEST is less v thania the the heat set exchanger in the boiler loop. The boiler loop pump switched on since the SUTEST temperature is less value of 50 ◦C. The fourth mode is the heat being taken out, actually an open loop that considers the than the set value of 50 °C. The fourth mode is the heat being taken out, actually an open loop that considers the working fluid delivered to the house to remove thermal energy from the UTEST. The Sustainability 2020, 12, 8686 4 of 19

Sustainability 2020, 12, x FOR PEER REVIEW 4 of 19 working fluid delivered to the house to remove thermal energy from the UTEST. The heat is transferred heatvia radiant is transferred floor heating via radiant (tubes floor with heating hot water (tubes buried with insidehot water the buried floor) to inside the house. the floor) Working to the fluidhouse is. Workingresponsible fluid for is transferring responsible thermal for transferring energy as therma loopsl (see energy Figure as 2loopsa). (see Figure 2a).

(a)

(b)

(c)

(d)

Figure 2. 2.Proposed Proposed system system diagrams. diagrams (a) Solar-assisted. (a) Solar house-assisted heating using house an underground heating using thermal an undergroundenergy storage thermal system; (energyb) House storage dimension; system; (c) ( 1.b) TheHouse surface dimension; layer (wood); (c) 1. The 2. Cement surface mortar; layer (wood);3. Insulation; 2. Cement 4. Concrete)); mortar; (d) Radiant 3. Insulation; ﬂoor hot 4. water Concrete)); tube dispositions. (d) Radiant floor hot water tube dispositions. Sustainability 2020, 12, 8686 5 of 19

The SUTEST is built underground to insulate the tank for a somewhat more reliable and less intense cold season as per underground conditions. Also, the temperature of the soil remains constant year-round. The cubic shape is constructed of concrete walls with polyurethane insulation. Figure2b showed the dimensions of the walls and window. The house is composed of walls, a roof, a window, and a radiant floor. The walls consist of four layers of materials: an internal layer of 20 mm gypsum wallboard, the second layer of 50 mm mineral fiber batt insulation, the third layer of 100 mm concrete, and an external layer of 10 mm cement mortar. The window consists of three layers of materials, an internal layer of 15 mm glass, the second layer of 12.7 mm air (cavity layer), and an external layer of 15 mm glass. The house’s base length, width, and height are 10.9 m, 10 m, and 3 m, respectively. The base width and the height of the window are 2.0 m and 1.5 m, respectively. The floor consists of four layers of materials: a surface layer of 10 mm wood, the second layer of 10 mm cement mortar, the third layer of 100 mm insulation (mineral fiber batt), and a bottom layer of 100 mm concrete; the area of the floor is 109 m2. The four layers of materials and the radiant floor are illustrated in Figure2c. The tubes are embedded in the cement mortar slabs. To distribute the temperature uniformly and create a comfortable environment for the occupants, the tubes are divided into four branches, illustrated in Figure2d. The mass flow rate of each branch is set to about 2.0 kg /s. A total tube length of 345.6 m, outer tube diameter of about 0.03 m, thickness of 0.003 m, and tube spacing of about 0.3 m are chosen. Materials’ thermal properties details are given in Table1.

Table 1. Main parameters for calculations.

The Thickness and Thermal Properties Description Thickness L Thermal Conductivity K Density ρ Speciﬁc Heat Resistance R (mm) (W/mK) (kg/m3) Cp (J/kg.K) (m2K/W) Cement mortar 10 0.93 1600 906 0.01075 Concrete 100 1.73 2235 1106 0.05780 Roof Insulation 50 0.0433 32 840 1.15473 Air layer 250 - - - 0.18 Gypsum ceiling 20 0.16 641 840 0.125 board Cement mortar 10 0.93 1600 900 0.01075 Concrete 100 1.73 2225 1106 0.05780 Walls Insulation 50 0.0433 91 840 1.15473 Gypsum wall 20 0.727 1602 840 0.02751 board Window Glass 15 0.756 2500 840 0.01984 Double Air (cavity 12.7 - - - 0.18 Glazing layer) Glass 15 0.756 2500 840 0.01984 Surface layer 10 0.16 700 1630 0.0625 Cement mortar 100 0.93 1600 900 0.10752 Floor Insulation 100 0.0433 91 840 2.30946 Concrete 100 1.73 2235 1106 0.05780 Cement mortar 10 0.93 1600 900 0.01075 Concrete 100 1.73 2235 1106 0.05780 UST Insulation 200 0.0433 91 840 4.61893 Concrete 100 1.73 2235 1106 0.05780 Insulation 206 0.0433 91 840 4.75750 CST Steel 5 45.3 7833 502 1.10374 Sustainability 2020, 12, 8686 6 of 19

2.2. Calculation/Theory

2.2.1. Solar Collector

The useful heat gain Qu of the ETC is calculated as provided by [33] as follows:

Qu = Ac.FR[(ατ).It UL(T Ta)] = mcp(Tco T ) (1) − ci − − ci where m and Ac are the water flow rate and the aperture area of the ETC, respectively. It is the solar radiation on the surface of the ETC and ατ is the cover transmittance absorptance. Tci,Tco and Ta are the inlet and outlet water temperature of the evacuated tube collector and the ambient temperature. UL is the overall heat loss coefficient of the collector. The collector heat removal factor FR, which is related to the collector area, overall heat loss coefficient, and mass flow rate is determined as: " # m.cp Ac.UL.F0 FR = 1 exp( ) (2) Ac.UL − − m.cp where F’ and m are the collector efficiency factor and mass flow rate of water in the collector loop.

2.2.2. Seasonal Underground Thermal Storage Tank An energy balance on the seasonal underground thermal storage tank (SUTEST) is expressed as:

dTs Ct = Qu + Qbol Qw Qpanel Qst hl (3) dt − − − − where Qbol and QW are the heat of boiler transfer to the SUTEST and the heat delivered from the SUTEST to the user. Qst-hl and Qpanel are the heat loss of the SUTEST and the radiant ﬂoor’s heat, respectively. Ct = Mcp; M and cp are the volume and the speciﬁc heat of the water in the SUTEST, respectively. Ts is the temperature of water in the SUTEST.

2.2.3. Residential House The heat balance model for a residential house can be viewed as four distinct processes: the outside surface heat balance, the wall conduction process, the inside surface heat balance, and the air heat balance. This section will describe in detail heat transfer processes for a residential house.

Outside Surface Heat Balance The outside surface heat balance for opaque surfaces consists of four heat transfer processes: net longwave radiation from the environment, convection heat transfer between exterior surface and outside air, short wave radiation, and conduction of the element. These heat transfer components are indicated as in Figure3, and the outside surface heat balance is expressed as:

q00 + q00 + q00 q00 = 0 (4) αsol LWR,o conv,o − ko

q00 q00 where αsol and LWR,o are absorbed direct and diffuse solar radiation heat flux, and net longwave 00 00 radiation is absorbed from surroundings. qconv,o and qko are convective heat flux exchange with outside air and conduction heat flux on the outside surface, respectively. Sustainability 2020, 12, x FOR PEER REVIEW 7 of 19

Sustainability 2020, 12, 8686 7 of 19 Sustainability 2020, 12, x FOR PEER REVIEW 7 of 19

Figure 3. Schematic of outside surface heat balance.

2.2.3.2 Wall Conduction ProcessFigure 3. Schematic of outside surface heat balance. Figure 3. Schematic of outside surface heat balance. " Wall ConductionThe heat conduction Process process through building walls is shown graphically in Figure 4, qki and 2.2.3.2" Wall Conduction Process q are the conduction heat fluxes at the inside and outside surface, and Tsi and Tos are00 the surface00 koThe heat conduction process through building walls is shown graphically in Figure4, qki and qko are the conduction heat ﬂuxes at the inside and outside surface, and T and T are the surface temperatures" temperaturesThe heat conduction on the inside process and outside through of building the wall. walls For building is shownsi heating graphicallyos load calculation,in Figure 4, itq mustki and be onassumed" the inside that and the outside wall conduction of the wall. process For building through heating multilayer load constructions calculation, it functions must be assumedas a one- q are the conduction heat fluxes at the inside and outside surface, and Tsi and Tos are the surface thatdimensionalko the wall conduction transient process. process E throughach layer multilayer material constructions is homogeneous, functions isotropic as a, one-dimensionaland has constant transienttemperatures process. on the Each inside layer and material outside is homogeneous,of the wall. For isotropic, building andheating has constantload calculation, thermal propertiesit must be thermal properties (i.e., k, and C p ). (i.e.,assumedk, ρ and thatC p the). wall conduction process through multilayer constructions functions as a one- dimensional transient process. Each layer material is homogeneous, isotropic, and has constant

thermal properties (i.e., k, and C p ).

FigureFigure 4. 4. SchematicSchematic ofof the the wall wall conduction conduction process process

TheThe most most current current thermal thermal load load calculation calculation methods methods of of building building constructions constructions are are the the transfer transfer functionfunction method, method, the the heat heatFigure balance balance 4. method,Schematic method, the theof radiantthe radiant wall time timeconduction series series method, method process and, and the the thermal thermal response response factorfactor method. method. In In this this study, study the, the thermal thermal response response factor factor method method is is used used as as the the method method of of choice choice for for The most current thermal load calculation methods of building constructions are the transfer calculatingcalculating heating heating loads. loads The. The Equation Equation for for heat heat conduction conduction in in a a layer layer of o buildingf building material material is is given given as as function method, the heat balance method, the radiant time series method, and the thermal response followsfollows [34 [34–40–40]:]: factor method. In this study, the thermal2 response factor method is used as the method of choice for ∂ T2 (x, t) 1 ∂T(x, t) calculating heating loads. The Equation forT heat(x,t conduction)= 1 T (x in,t )a layer of building material is given(5) as ∂x2 α ∂t (5) follows [34–40]: x 2  t  2T (x,t) 1 T (x,t)  (5) x 2  t Sustainability 2020, 12, 8686 8 of 19

T is the temperature at position (x) and time (t), and α is the layer material’s thermal diﬀusivity. The heat ﬂux at an arbitrary position x and time t based on Fourier’s of conduction is given as:

∂T(x, t) q00 (x, t) = k (6) − ∂x where K is the thermal conductivity of the layer material (W/mK). The solution of Equations (5) and (6) can be represented in terms of Laplace variable s relates the heat ﬂows and temperatures at both surface of the wall as: " # " # " #" # T (s) Tos(s) A(s) B(s) Tos(s) is = M(s) = (7) 00 ( ) 00 ( ) ( ) 00 ( ) qki s qko C s D s qko s

The Equation (7) can be re-written based on relating surface temperatures and heat ﬂows of both surfaces as follows: " # " #" # q00 (s) GX(s) G (s) Tos(s) ko = − Y (8) q00 (s) G (s) GZ(s) T (s) ki Y − is where GX(s), GY(s), GZ(s) and are the transfer functions of outside, cross, and inside heat conduction of construction, respectively. 00 The outside surface heat ﬂux qko for time t in terms of current and past boundary temperatures as inputs and the response factors is expressed as:

Xn Xn q00 (t) = XoTos,t XjTos,t jθ + YoTis,t + YjTis,t jθ (9) ko − − − − j=1 j=1 and for the inside surface heat ﬂux is as follows:

Xn Xn q00 (t) = ZoTis,t + ZjTis,t jθ YoTos,t YjTos,t jθ (10) ki − − − − j=1 j=1

Xj, Yj, and Zj are external response factors, cross-response factors, and internal response factors.

Heat Balance of Inside Surface The inside heat balance consists of four heat transfer components: wall conduction, convection from air zone to the inside surface, short wave radiation, and longwave radiant interchanger. These four components are shown schematically in Figure5. The inside heat balance for each surface is expressed as:

q00 + q00 + q00 + q00 + q00 q00 = 0 (11) LWX SW LWS sol conv,i − ki

00 00 00 where qLWX, qSW, and qLWS are net longwave radiation from zone surfaces, net short-wave radiation 00 00 from lights, and net longwave radiation from equipment in the zone. qsol and qconv,i are transmitted solar radiation absorbed by zone surface and convective heat ﬂux from the air zone to the inside surface. SustainabilitySustainability2020 2020,,12 12,, 8686 x FOR PEER REVIEW 99 ofof 1919

FigureFigure 5. 5. InsideInside surface surface heatheat transfer transfer components. components. Room Air Heat Balance 2.2.3.4 Room Air Heat Balance The room air heat balance consists of four heat transfer components: convection from zone air toThe inside room surfaces, air heat transport balance consists of outside of airfour directly heat transfer into the components: zone by infiltration convection and from ventilation, zone air convectionto inside surfaces, heat transfers transport from of internal outside sources, air directly and into heat the transfer zone byrate infiltration due to the and heating ventilation, panel. Theconvection room air heat heat transfers balance from is calculated internal as sources follows:, and heat transfer rate due to the heating panel. The room air heat balance is calculated as follows: dTr Cair dT = Qpanel Qconv,i + QCE QIV (12) C dt r  Q − Q  Q − Q (12) air dt panel conv,i CE IV where Cair and Qconv,i are heat capacity of air in the room and convection heat transfer from the room airwhere to the C insideair and surfaces. Qconv,i areQCE heatand capacityQIV are of heat air in transfer the room from and internal convection sources, heat i.e., transfer people, from lights, the equipment, etc., and heat gain due to infiltration. room air to the inside surfaces. Q and Q are heat transfer from internal sources, i.e., people, Based on the calculated overallCE heat transferIV coefficient, the heat flux through the radiant floor is calculatedlights, equipment, as follows: etc., and heat gain due to infiltration. Up − Based on the calculated overall heat transfer coefficient, thempcp heat flux through the radiant floor Q = 4mpcp(T Tr)(1 e ) (13) is calculated as follows: panel pi − − where T and T are the inlet water temperature of the radiant floor and room air temperature. m and pi r U p p

Up are the mass flow rate of water through the radiant floor and overallm pc p heat transfer coefficient of(13 the) Q  4m c (T T )(1 e ) radiant floor. panel p p pi r

whereA MATLABTpi and Tr codeare the with inlet a derivedwater temperature mathematical of modelthe radiant was developedfloor and room in this air work temperature. to calculate mp theand multilayer Up are the thermalmass flow response rate of water factors through for a residential the radiant house. floor and The overall flow charts heat transfer of the calculation coefficient programof the radiant are shown floor. in Figures6 and7, respectively. To perform this calculation, the accurate selection of frequencyA MATLAB points code is essential. with a derived It is necessary mathematical to determine model the was number developed of N frequencyin this work points to calculate and the required frequency range [10 n1/s, 10 n2/s]. In general, n = 7 10, n = 2 4 and N = 10 (n n ) + 1. the multilayer thermal response− factors− for a residential1 house÷ . 2The ÷flow charts of ×the 1calculation− 2 However,program are the shown values in of Figures n1, n2, 6and and N7, canrespectively. be changed To perform depending this on calculation, materials the such accurate as lightweight selection materials,of frequency medium-weight points is essential materials,. It is and necessary heavyweight to determine materials. the To number expand of the N computationfrequency points accuracy, and thethe frequency required frequency features from range the [10 N1−thn1/s, ~ N102−thn2/s]. frequency In general, point n1 within = 7 ÷ 10, the n N2 = frequency2 ÷ 4 and N points = 10 are× (n carefully1 − n2) + 1. chosen to create the polynomial s-transfer functions, where N 1 and N N. Throughout the However, the values of n1, n2, and N can be changed depending1 ≥ on materials2 ≤ such as lightweight calculationmaterials, process,medium the-weight values materials of N1 and, and N2 are heavyweight adjusted until materials. the computation To expand precision the is computation not further enhanced.accuracy, the The frequency coefficients features of polynomial from the s-transfer N1th ~ N functions2th frequency change point with within the di thefference N frequency of parameters points n,ar m,e carefully n1, n2, N 1, chosenN2. In orderto create to check the polynomial whether the s multilayer-transfer functions, thermal response where factorsN1 ≥ 1 constructions and N2 ≤ N. Throughout the calculation process, the values of N1 and N2 are adjusted until the computation precision is not further enhanced. The coefficients of polynomial s-transfer functions change with the difference of parameters n, m, n1, n2, N1, N2. In order to check whether the multilayer thermal response Sustainability 2020, 12, x FOR PEER REVIEW 10 of 19 factors constructions are accurate or not, it is important to consider whether the U-factor of multilayer constructions is equivalent to the sum of its thermal response factors used in equation (14).

M M M X  Y  Z U  j  j  j (14) j1 j1 j1

The 5th order polynomial s-transfers, GX(s), GY(s), GZ(s) for the outside conduction of heat, across heat conduction, and inside heat conduction of the walls, roof, window, and SUTEST were functioned by the frequency domain regression (FDR) process. Thermal response factors of the walls, roof, window, and SUTEST, which were calculated based on polynomial s-transfers GX(s), GY(s), GZ(s) are given in Table 2. In addition, the values of n1, n2, and N, the error percentage (EP) concerning the U- factor, and the total thermal response factors of the outside heat conduction, across heat conduction, and inside heat conduction are also given as in Table 2.

Table 2. Thermal response factor of the wall, roof, window, and seasonal underground thermal energy storage tank (SUTEST).

X(s) Y(s) Z(s) Frequency Points N (W/m2K) (W/m2K) (W/m2K) ∑ 0.79949473 0.79949720 0.79949472 N = 9 × (n1 − n2) +1 Wall Uwall 0.79949471 0.79949471 0.79949471 (n1 = 9, n2 = 3) EP 2.5 × 10−6% 3.11 × 10−4% 1.25 × 10−6% ∑ 0.6543432181 0.6543432024 0.6543432030 N= 9 × (n1 − n2) +1 Roof Uroof 0.6543303583 0.6543303583 0.6543303583 Sustainability 2020, 12, 8686 (n1 = 9, n2 = 3) 10 of 19 EP 1.96 × 10−3% 1.96 × 10−3% 1.96 × 10−3% ∑ 4.552034304 4.550037054 4.552034304 N= 11 × (n1 − n2) +1 are accurateWindow or not,U itwindow is important 4.552075747 to consider 4.552075747 whether the U-factor4.552075747 of multilayer constructions is (n1 = 6, n2 = 1) equivalent to the sum ofEP its thermal9.1 × 10 response−4% factors4.47 × 10 used−4% in equation4.14 × 10−3 (14).%

∑ 0.210735723M 0.210964185M M 0.210735831 Underground X X X N = 9 × (n1 − n2) +1 UUST 0.210735720X = 0.210735720Y = Z =0.210735720U (14) storage tank j j j (n1 = 9, n2 = 3) EP 1.42 × 10j=−41 % j=1 0.1%j =1 5.26 × 10−5%

FigureFigure 6. Flow 6. Flow chart chart for for thermal thermal response factor factor calculations. calculations.

The 5th order polynomial s-transfers, GX(s), GY(s), GZ(s) for the outside conduction of heat, across heat conduction, and inside heat conduction of the walls, roof, window, and SUTEST were functioned by the frequency domain regression (FDR) process. Thermal response factors of the walls, roof, window, and SUTEST, which were calculated based on polynomial s-transfers GX(s), GY(s), GZ(s) are given in Table2. In addition, the values of n1, n2, and N, the error percentage (EP) concerning the U-factor, and the total thermal response factors of the outside heat conduction, across heat conduction, and inside heat conduction are also given as in Table2.

Table 2. Thermal response factor of the wall, roof, window, and seasonal underground thermal energy storage tank (SUTEST).

X(s) Y(s) Z(s) Frequency Points N (W/m2K) (W/m2K) (W/m2K) P 0.79949473 0.79949720 0.79949472 N = 9 (n n ) +1 Wall U 0.79949471 0.79949471 0.79949471 × 1 − 2 wall (n = 9, n = 3) EP 2.5 10 6% 3.11 10 4% 1.25 10 6% 1 2 × − × − × − P 0.6543432181 0.6543432024 0.6543432030 N= 9 (n n ) +1 Roof U 0.6543303583 0.6543303583 0.6543303583 × 1 − 2 roof (n = 9, n = 3) EP 1.96 10 3% 1.96 10 3% 1.96 10 3% 1 2 × − × − × − P 4.552034304 4.550037054 4.552034304 N= 11 (n n ) +1 Window U 4.552075747 4.552075747 4.552075747 × 1 − 2 window (n = 6, n = 1) EP 9.1 10 4% 4.47 10 4% 4.14 10 3% 1 2 × − × − × − P 0.210735723 0.210964185 0.210735831 Underground N = 9 (n n ) +1 U 0.210735720 0.210735720 0.210735720 × 1 − 2 storage tank UST (n = 9, n = 3) EP 1.42 10 4% 0.1% 5.26 10 5% 1 2 × − × − Sustainability 2020, 12, 8686 11 of 19 Sustainability 2020, 12, x FOR PEER REVIEW 11 of 19

FigureFigure 7. Flow 7. Flow chart chart for for the the calculation calculation of anan undergroundunderground thermal thermal energy energy storage storage system. system.

TheThe initialinitial inlet temperature values values of of collector collector TciT areci are the thesame same as the as ambient the ambient temperature temperature Ta. In Tthea. Inunderground the underground thermal thermal storage storage tank, the tank, initial the water initial temperature water temperature value Tsi value is 50 °C. Tsi Theis 50 initial◦C. The mass initial flow massrate value flow rate is considered value is considered as 0.05 kg/s. as 0.05 The kg connecting/s. The connecting pipe heat pipe loss heat between loss between the underground the underground thermal thermalstorage storagetank and tank the radiant and the floor radiant is neglected. floor is neglected. Therefore, Therefore,the underground the underground thermal storage thermal tank storage’s water tank’stemperature water temperatureis similar to the is similarinlet tempe to therature inlet of temperature the radiant floor of the. The radiant bottom floor. surfaces The and bottom the side surfaces of the andradiant the sidefloor of are the correctly radiant floorinsulated. are correctly The initial insulated. temperature The initialof the temperaturehouse is 22.9 of °C. the The house inside is 22.9 surface◦C. 2 Theconvection inside surface coefficients convection of the house coefficients are constant. of the house They were are constant. chosen to They be 4.6 were W/m chosen2K for towalls, be 4.6 1.5 W W/m/m K2K 2 2 forfor walls, the roof 1.5, and W/m 6 W/mK for2K the for roof, the floor and, 6 respectively. W/m K for theThe floor, adjacent respectively. ground of The the adjacentstorage tank ground is expected of the storageto have tank the same is expected configuration to have and the sameconstant configuration thermo-physical and constant characteristics thermo-physical. The ground characteristics. temperature Thewas ground chosen temperatureto be 16.5 °C. wasThere chosen are no tointernal be 16.5 heat◦C. sources There are or domestic no internal hot heat water sources supply or to domestic the user. hotThe watersimulation supply was to theperformed user. The with simulation the time wasstep performed of 120 s. This with is thethe timesmallest step time of 120 step s. Thisthat can is the be smallest satisfied timewith step the thatconvergence can be satisfied requirement with theof Equation convergence (14). requirementThe simulation of Equation input on (14).whether The findings simulation consist input of onglobal whether solar findings irradiance consist and ofambient global solar temperature irradiance is shown and ambient in Figure temperature 8. In this is simulation, shown in Figure the heat8. Instabilities this simulation, expressed the concerning heat stabilities response expressed factors concerningthat are solved response for each factors timethat of the are day. solved The for solution each timemethod of the may day. be Theiterative solution (initial method guess of may the besurface iterative temperatures (initial guess and ofheat the fluxes surface are temperaturesupdated until andthey heatconverge) fluxes. areA check updated on the until solution they converge).validity is obtained A check onby thesolving solution a steady validity-state isproblem obtained Equation by solving (15). a steady-state problem Equation (15). q U(t  t ) q steady= U(t is tosos) ((15)15) steady is − Sustainability 2020, 12, x FOR PEER REVIEW 12 of 19 Sustainability 2020, 12, 8686 12 of 19 Sustainability 2020, 12, x FOR PEER REVIEW 12 of 19 1000 40 Global solar irradiance 1000 4035 GlobalAmbient solar temperature irradiance

)

2 800 35 Ambient temperature 30

)

2 800 600 3025

C) 600 25 o 20

400 C) 20 o 400 15

200 1510

Temperature ( Temperature

Global solar irradiance (W/m irradiance solar Global 200 10 5 ( Temperature

Global solar irradiance (W/m irradiance solar Global 0 5 0 0 0 4 8 12 16 20 24 Time (hr) 0 0 4 8 12 16 20 24 Figure 8. Global solar irradianceTime (hr) and ambient temperature. FigureFigure 8. 8.GlobalGlobal solar solar irradiance irradiance andand ambient ambient temperature. temperature. 3. Results and Discussion 3. Results and Discussion 3. ResultsTo satisfy and Discussionthe occupants’ comfort and health, the minimum room temperature was set to be 22 To satisfy the occupants’ comfort and health, the minimum room temperature was set to be °C whereasTo satisfy the the maximum occupants’ room comfort temperature and health was, the set minimum to be 25 room°C. This temperature means that was the set room to be air22 22 C whereas the maximum room temperature was set to be 25 C. This means that the room air °Ctemperature ◦whereas thewas maximum retained between room temperature 22 °C to 25 was°C. On set the to beother 25 hand,°C.◦ This an meanseasiness that dead the band room is airset temperature was retained between 22 C to 25 C. On the other hand, an easiness dead band is set temperaturefrom 22 °C to was 25 °Cretained to create between a hysteresis 22 ◦°C heatingto 25 ◦°C. cycle. On the The other control hand, procedure an easiness of the dead radiant band floor is set is from 22 C to 25 C to create a hysteresis heating cycle. The control procedure of the radiant floor is fromsimple. 22 The◦°C to pump 25 ◦°C of to the create radiant a hysteresis floor loop heating was based cycle. on The the control sensor proceduresignal, this of sensor the radiant was mounted floor is simple. The pump of the radiant floor loop was based on the sensor signal, this sensor was mounted simple.inside the The room. pump The of the radiant radiant floor floor loop loop pump was basedis switched on the onsensor when signal, the room this sensor air temperature was mounted fell inside the room. The radiant floor loop pump is switched on when the room air temperature fell below insidebelow the22 °C room. and Theremain radiants on untilfloor the loop room pump air istemperature switched on reache whens 25the °C, room at which air temperature point it will fell be 22 C and remains on until the room air temperature reaches 25 C, at which point it will be switched belowswitched◦ 22 °Coff. and If the remain temperatures on until decreases the room below air temperature 22 °C, a fresh reache◦ cycles 25 begins. °C, at whichThe oscillation point it will of thebe off. If the temperature decreases below 22 C, a fresh cycle begins. The oscillation of the room air switchedroom air temperatureoff. If the temperature during the decreases day is shown below◦ in 22Figure °C, a9 a.fresh As indicatedcycle begins. in Figure The oscillation 9a, the room of the air temperature during the day is shown in Figure9a. As indicated in Figure9a, the room air temperature roomtemperature air temperature intensely duringoscillated the between day is shown 00:00 and in Figure 08:30, and9a. As then indicated slowly oscillatedin Figure until9a, the about room 16:30 air intensely oscillated between 00:00 and 08:30, and then slowly oscillated until about 16:30 and then temperatureand then strongly intensely oscillated oscillated until between about 24:00 00:00. This and is 0 8:30,due to and the then oscillat slowlying ofoscillated the ambient until temperature about 16:30 strongly oscillated until about 24:00. This is due to the oscillating of the ambient temperature leading andlead thingen to strongly the change oscillated of the until heat aboutload of 24:00 the .room. This is due to the oscillating of the ambient temperature to the change of the heat load of the room. leading to the change of the heat load of the room. 30 29 Temperature 30 28 29 Temperature 27

o 28 26 27

o 25 26 24 25 23 24 22 23 21 22 20 21 19 20

Room air temperature ( 18 19 17

Room air temperature ( 18 16 17 15 16 0 4 8 12 16 20 24 15 Time (hr) 0 4 8 12 16 20 24 (Timea) (hr)

Figure(a 9.) Cont. SustainabilitySustainability 20202020,, 1212,, 8686x FOR PEER REVIEW 1313 ofof 1919

30 30 Inside surface wall temperature 28 28 Inside surface roof temperature

C) 26 26

o Inside surface window temperature 24 24

C) 22 22 o 20 20 18 18 16 16 14 14 12 12 10 10 8 8

Inside surface temprature ( temprature surface Inside 6 Outside surface window temperature 6

4 Outside surface roof temperature 4 ( temprature surface Outside 2 Outside surface wall temperature 2 0 0 0 4 8 12 16 20 24 Time (hr) (b)

5.0 Qust-hl 4.5 Qsol 4.0 Qr-hl 3.5 Qpanel 3.0 Qbol 2.5 2.0 1.5

Energy (kWh) 1.0 0.5 0.0 -0.5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Time (hr) (c)

38 52 36 Solar energy Auxiliary energy 50 34 48 32 30 46 28 44 26 42 24 22 40

Energy (kWh) Energy 20 38 18 36

Solar fraction(%) Solar 16 Solar fraction 34 14 12 32 10 30 50 100 200 300 400 500 600 Insulation thickness of underground storage tank(mm)

(d)

Figure 9. Cont. Sustainability 20202020,, 1212,, 8686x FOR PEER REVIEW 14 of 19

38 52 36 Solar energy Auxiliary energy 50 34 Solar fraction 48 32 30 46 28 44 26 42 24 22 40

Energy (kWh) Energy 20 38

18 36 fraction(%) Solar 16 34 14 12 32 10 30 1.2 5 10 20 30 40 50 3 Volume of underground storage tank(m ) (e)

45 80 Solar energy Auxiliary energy 75 40 Solar fraction 70 35 65 60 30 55 25 50

Energy(kWh)

20 45 fraction(%) Solar 40 15 35 10 30 20 25 30 35 40 45 50 2 Collector area(m ) (f)

Figure 9.9.Solar-assisted Solar-assisted heating heating system system temperature temperature oscillation oscillation and parametric and parametric effects. (a) The effects. room ( aira) temperatureThe room air oscillation temperature during oscillation the day; ( bduring) The outside the day; surfaces (b) The temperature outside surfaces oscillation temperature and inside roomoscillation surfaces and during inside the room day; surfaces (c) Solar-assisted during heatingthe day; system (c) Solar heat-assisted transfer forheating a residential system house heat withtransfer an underground for a residential thermal storage house tank; with (d) Underground an underground thermal thermal storage tank storage effect of tank; insulation (d) thicknessUnderground on system thermal efficiency storage during tank the day; effect (e )of Volume insulation effect of thickness underground on thermal system storage efficiency tank onduring system the eff ectiveness day; (e) Volumethroughout effect the day; of underground(f) Solar collector thermal area eff ect storage on method tank compactness on system throughouteffectiveness the throughout day. the day; (f) Solar collector area effect on method compactness throughout the day. Figure9b describes the temperature oscillation of the outside surfaces and inside surfaces of the room during the day. As seen in Figure9b, the dissimilarity between the inside surface temperatures Figure 9b describes the temperature oscillation of the outside surfaces and inside surfaces of the and, the room air temperature ranges from 0.5 C to 2 C, while the variations regarding the temperature room during the day. As seen in Figure 9b, the◦ dissimilarity◦ between the inside surface temperatures of the outside surfaces and the ambient temperature range from 2 C to 5 C. This difference strongly and, the room air temperature ranges from 0.5 °C to 2 °C, while◦ the◦ variations regarding the decreased from 09:00 to 16:00, and the increased ambient temperature led to the room’s heat capacity temperature of the outside surfaces and the ambient temperature range from 2 °C to 5 °C. This decreasing. The temperature oscillation of the surfaces is not the same. This is due to the surfaces of difference strongly decreased from 09:00 to 16:00, and the increased ambient temperature led to the the room having a convection coefficient, and different building materials. room’s heat capacity decreasing. The temperature oscillation of the surfaces is not the same. This is Figure9c shows the solar-assisted heating system heat transfer trend for the residential houses due to the surfaces of the room having a convection coefficient, and different building materials. during the day. In this work, an underground thermal storage tank is 10 m3 and is built of concrete Figure 9c shows the solar-assisted heating system heat transfer trend for the residential houses with polyurethane insulation of 200 mm were taken into consideration. The useful heat gains heat during the day. In this work, an underground thermal storage tank is 10 m3 and is built of concrete flux Q of the solar collector is conveyed to the underground thermal storage tank. From 09:00 to with polyurethaneu insulation of 200 mm were taken into consideration. The useful heat gains heat 16:00 the auxiliary heat flux Qbol of the boiler was transported to the underground thermal storage flux Qu of the solar collector is conveyed to the underground thermal storage tank. From 09:00 to Sustainability 2020, 12, 8686 15 of 19

tank during 00:00 to 09:00 and from 21:00 to 24:00. The radiant floor heat flux Qpanel supplied into the room slightly changed between 00:00 and 08:30, decreased slowly until about 15:00, and then increased again. This is because of the change in ambient temperature and the fluctuation of the global solar irradiance, leading to the change of the room’s heat load Qr hl. The heat flux of the heat loss Qust hl − − of the underground thermal storage tank slightly changed. That is because the ground temperature is constant, and the water temperature in the underground thermal storage tank slightly changed during the day. The solar fraction is usually used to measure the solar heating system’s efficiency, which means the fraction of the total heating capacity provided by the sun. The valuable heat gain amount Qu of the solar collector, the auxiliary heat amount Qbol of the boiler, the heat amount of the radiant floor Qpanel, the heat load of the room Qr hl, the heat loss amount Qust hl of the underground − − thermal storage tank, and the solar fraction for during the day are given in Table3.

Table 3. Simulation results during the day.

Qu (kWh) Qbol (kWh) Qpanel (kWh) Qr hl (kWh) Qust hl (kWh) Solar Fraction (%) − − 21.27 25.73 43.21 42.25 4.09 45.8

Figure9d shows the e ffect of the underground thermal storage tank0s insulation thickness on system effectiveness throughout the day. When the insulation thickness ranges from 50 mm to 200 mm, the amount of extra energy Qbol sharply decreases from 36.5 kWh to 25.41 kWh, the useful heat gain Qu decreases only slightly, and the solar fraction strongly increases from 36.89% to 45.8%. This is because the increase in insulation thickness leads to a decrease in the underground thermal storage tank’s heat loss. When the insulation thickness grows larger than 200 mm, the amount of auxiliary energy Qbol continued to decrease, but at a much lower rate, the useful heat gain Qu continued to slightly decrease, and the solar fraction tends to be steady. This is because the increase in water temperature is lower than the increase in the U-factor of the underground thermal storage tank, while the heat loss of the underground thermal storage tank decreases slowly. Figure9e shows the e ffect of the underground thermal storage tank’s volume on system performance during the day. When the underground thermal storage tank volume ranges from 3 3 1.2 m to 5 m , the amount of auxiliary energy Qbol slightly increases, the useful heat gain Qu increases from 19.39 kWh to 21 kWh, and the solar fraction sharply increases from 43.9% to 46.1%. For tank 3 3 volume sizes from 5 m to 50 m , the number of auxiliary energies Qbol increases gradually until about 3 10 m and then increases sharply, while the useful heat gain Qu tends to be steady. The solar fraction slightly decreases until about 10 m3 and then strongly decreases. This is because the collector remains the same while the underground thermal storage tank volume increases. At the underground thermal storage tank, 1.2 m3 did not have enough thermal mass to store as much useful heat gain as the larger underground thermal storage tank. The tanks 5 m3 and larger were able to store more useful heat gain transferred to the room via the radiant floor. The room model with an underground thermal storage tank 5 m3 could supply more heat to the room via the radiant floor, which lowers the sum of heat delivered by the supporting boiler. However, once the underground thermal storage tank’s volume increased above 5 m3, the quantity of heat delivered by the supporting boiler increased. This can be explained by the required temperature of water in the underground thermal storage tank not being less than 50 ◦C. Therefore, the volume increase leads to an increase in the storage mass, and more energy is required to maintain this temperature. Thus, although the 50 m3 tank can constitute the total stored energy, the temperature of that larger tank is not as high. Therefore, further increases in tank size were not advantageous. The large volume of the underground thermal storage tank is meaningful only when a large solar collector area accompanies it. Figure9f demonstrates the solar collector area’s consequences on system e fficiency throughout 2 2 the day. Once the collector area ranges from 20 m to 35 m , the amount of auxiliary energy Qbol strongly decreases from 29.86 kWh to 16.86 kWh, the useful heat gain Qu increases from 15.84 kWh to 28.85 kWh, and the solar fraction sharply increases from 34.66% to 63.12%. This is because the Sustainability 2020, 12, 8686 16 of 19 greater the area of collectors, the more significant the amount of useful heat gain that can be captured, stored, and distributed into the room. When the collector area grows more massive than 35 m2, the number of auxiliary energies Qbol tends to be steady, while the useful heat gain Qu continued to upsurge and the solar fraction slowly increases. This is due to the simulation calculated during the day. Therefore, in the earlier morning, the energy amount required to maintain the underground thermal storage tank’s water temperature is not less than 50 ◦C, so this energy was provided by the auxiliary boiler. However, after that period, it was provided by the useful heat gain Qu of the solar collectors.

4. Conclusions In the present study, the solar-assisted heating system for a residential house with a seasonal underground thermal storage tank is developed, and the following conclusion could be obtained. This work proposes a solar-assisted heating system for a residential house with SUTEST, in which the heat load of the house and heat loss of the SUTEST were evaluated by the thermal response factor method. A MATLAB program was developed, depending on the basic mathematical model to compute the thermal response factors. The polynomial s-transfers of building construction were also estimated. The optimal insulation thickness of SUTEST should be better or equal to 200 mm. This ensures the highest solar fraction. The optimal volume of the SUTEST was determined at 5 m3. This work also demonstrated that the large volume of the underground thermal storage tank is meaningful only when a large solar collector area accompanies it. For this study, we recommend that a residential house’s solar-assisted heating system with a thermal storage tank should be replaced by the solar-assisted heating system with a boiler and a SUTEST. This will become the cause of the rise in solar fraction and a decrease in SUTEST heat loss. The simulations were performed on dissimilar days in terms of weather conditions, i.e., a clear day, intermittently cloud sky, and overcast sky to calculate the system operation with a constant mass ﬂow rate for the collector loop. The simulated results showed that the obtained solar fraction was 45.8%, 17.26%, and 0%.

Author Contributions: Methodology, validation, formal analysis, investigation, L.M.N. Writing—original draft preparation and writing—review and editing, W.R.; supervision, funding acquisition, and project administration, Y.C.P. All authors have read and agreed to the published version of the manuscript. Funding: The technology innovation program supported this work (No. 20182020109700, development of a hybrid cooling system for refrigeration truck with an ejector) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea), by the National Research Foundation of Korea (No. 2020R1A2C1011871), and by the project of 2021 funded by Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Vietnam. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

2 Ac Aperture area of collector (m ) Cp Specific heat (J/kg. K) Cair Heat capacity of air in the room (J/K) FR Collector heat removal factor 2 It Solar radiation (W/m ) K Thermal Conductivity (W/mK) L Thickness (mm) N Number of frequency points M Volume of water in the SUTEST (m3) m Mass flow rate of collector loop (kg/s) mp Mass flow rate of the radiant floor (kg/s) Qbol Heat of boiler (W) Qpanel Heat of radiant floor (W) Sustainability 2020, 12, 8686 17 of 19

Qr-hl Room heat load (W) Qu Useful solar heat gain (W) Qust-hl Heat loss of storage tank (W) Qconv,i Convection heat transfer from the room air to the inside surfaces (W) QCE Heat transfer from internal sources, i.e., people, lights, equipment, etc. (W) QIV Heat gain due to infiltration (W) q00 2 αsol Absorbed direct and diffuse solar radiation heat flux (W/m ) 00 2 qLWR,o Net longwave radiation absorbed from surroundings (W/m ) 2 qconv00 ,o Convective heat flux exchange with outside air (W/m ) q00 2 ko Outside surface heat flux (W/m ) q00 2 ki Inside surface heat flux (W/m ) 00 2 qLWX Net longwave radiation from zone surfaces (W/m ) 00 2 qSW Short wave radiation from lights (W/m ) 00 2 qLWS Net longwave radiation from equipments in zone (W/m ) q00 2 sol Transmitted solar radiation absorbed by zone surface (W/m ) q00 2 conv,i convective heat flux from the air zone to inside surface (W/m ) R Resistance (m2K/W) TES Thermal energy storage STES Seasonal thermal energy storage SUTEST Seasonal underground thermal energy storage tank UTEST Underground thermal energy storage tank Ta ambient temperature (◦C) Tis Inside surface temperature (◦C) Tos Outside surface temperature (◦C) Tci Collector inlet temperature (◦C) Tco Collector outlet temperature (◦C) Ts Temperature of water in the SUTEST (◦C) Tsi Storage tank inlet temperature (◦C) Tr Room air temperature (◦C) Tpi Inlet water temperature of the radiant floor (◦C) UST Underground storage tank 2 UL overall heat loss coefficient of the collector (W/m K) Up overall heat transfer coefficient of the radiant floor (W/m2K) ρ Density of water (kg/m3) ατ cover transmittance absorptance

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